I am looking to solve a constrained optimization problem where I know the bounds on some of the variables (specifically a boxed constraint). Does anyone know of a package that can handle this?

I am looking to solve a constrained optimization problem where I know the bounds on some of the variables (specifically a boxed constraint).

$$ \arg \min_u f(u,x) $$

subject to

$$ c(u,x) = 0 $$ $$ a \le d(u,x) \le b $$

where $u$ is a vector of design variables, $x$ is a vector of state variables, and $c(u,x)$ is an equality constraint (usually a PDE). The lower and upper constraints $a$ and $b$ may be spatially variable.

Which packages can handle systems of this form?